K13a2840
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a2840/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+11 t^3-43 t^2+88 t-109+88 t^{-1} -43 t^{-2} +11 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13a2840/Conway Polynomial |
| Determinant | 395 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-5 z^2 a^6-2 a^6+3 z^6 a^4+6 z^4 a^4+4 z^2 a^4+a^4-z^8 a^2-2 z^6 a^2-2 z^4 a^2-z^2 a^2+2 z^6+3 z^4+z^2+1-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{12}+3 a^2 z^{12}+10 a^5 z^{11}+21 a^3 z^{11}+11 a z^{11}+15 a^6 z^{10}+31 a^4 z^{10}+32 a^2 z^{10}+16 z^{10}+14 a^7 z^9+10 a^5 z^9-15 a^3 z^9+a z^9+12 z^9 a^{-1} +9 a^8 z^8-15 a^6 z^8-72 a^4 z^8-85 a^2 z^8+5 z^8 a^{-2} -32 z^8+4 a^9 z^7-22 a^7 z^7-53 a^5 z^7-46 a^3 z^7-48 a z^7-28 z^7 a^{-1} +z^7 a^{-3} +a^{10} z^6-15 a^8 z^6-7 a^6 z^6+42 a^4 z^6+60 a^2 z^6-11 z^6 a^{-2} +16 z^6-7 a^9 z^5+16 a^7 z^5+55 a^5 z^5+51 a^3 z^5+43 a z^5+22 z^5 a^{-1} -2 z^5 a^{-3} -2 a^{10} z^4+11 a^8 z^4+24 a^6 z^4+5 a^4 z^4-17 a^2 z^4+8 z^4 a^{-2} -3 z^4+4 a^9 z^3-5 a^7 z^3-18 a^5 z^3-12 a^3 z^3-11 a z^3-7 z^3 a^{-1} +z^3 a^{-3} +a^{10} z^2-5 a^8 z^2-14 a^6 z^2-8 a^4 z^2+2 a^2 z^2-2 z^2 a^{-2} -a^9 z+a^5 z-a^3 z-a z+a^8+2 a^6+a^4+1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
